Eulerian cycle

eulerian cycle

An Eulerian cycle is any cycle in a graph that visits each and every link (or edge) exactly once.

Necessary condition for an Eulerian cycle

The following condition was proved by Euler.

necessary condition for an eulerian cycle

A necessary condition for the existance of an Eulerian cycle is that all nodes in the graph have an [[#Even degree]].

even degree nodes

A node has an even degree when it spans an even number of edges (links).